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Brookline 10th-grader Ashley Olafsson sleeps with her cellphone under her pillow so she doesn’t miss “emergency’’ texts — “like if a friend broke up with her boyfriend.’’ Stephanie Kimball of Waltham, 14, is also available for urgent overnight correspondence, such as, “Hey, seeing if you’re awake.’’ Dedham ninth-grader Courtney Johnson gets as many as 100 texts while in bed. “I just don’t feel like myself if I don’t have my phone near me or I’m not on it,’’ she said.

Sure, all that middle-of-the-night communication leaves them tired, but as Olafsson explained, “It’s impolite not to respond if someone is coming to you with their problems.’’

With teenagers sending and receiving an average of 3,276 texts per month in the last quarter of 2010, according to the most recent statistics from the Nielsen Co., it’s no wonder that Michael Rich, director of Children’s Hospital Boston’s Center on Media and Child Health, is starting to see young patients who come in exhausted by being “on call’’ or semi-alert all night as they wait for their phones to vibrate or ring with a text.

He and his patients’ parents were initially baffled by the children’s increased sleepiness because bedtimes hadn’t changed, he said. “Who would think to ask a kid, ‘Do you sleep with your phone under your pillow?’ To us, it sounds like torture.’’

Children who text late into the night do not fall asleep as well, he said, and they don’t enter the deep sleep of Stage 4 REM sleep, “which is crucial to moving experiences and lessons of the day from short-term into long-term memory — in other words, completing the learning process.’’

Anticipating texts, Rich explained, leads to a bad night’s sleep in the same way as an early morning flight or other predawn obligation. “You’re so focused on not screwing up your wake-up that you don’t sleep as well.’’

A Pew Research Center study from 2010 reported that more than four out of five teens with cellphones sleep with the phone on or near the bed, sometimes falling asleep with it in their hands in the middle of a conversation. Pew researchers did not ask whether the phones were on, but Amanda Lenhart, a senior research specialist, said “many expressed reluctance to ever turn their phones off.’’

Researchers at the JFK Medical Center sleep laboratory in Edison, N.J., found in a 2010 study that teens sent an average of 33.5 e-mails and texts overnight and that their sleep was affected. A National Sleep Foundation study released this month found that almost one in five teens ages 13-18 are awakened by a phone call, text message, or e-mail at least a few nights a week.

Dr. Scott Frank, director of the Master of Public Health Program at Case Western Reserve University School of Medicine, has seen the effects of all that late-night texting. In a 2009 study, he found that “hyper-texting’’ teens — those who texted 120 times or more on an average school day — were more than 60 percent more likely to sleep less than seven hours per night and to doze off in class than those who were not hyper-texters.

“These teens were also more than 60 percent more likely to miss more school because of illness and to have poor academic performance,’’ he wrote in an e-mail. “Teens were also 25 percent more likely to report high levels of stress and 40 percent more likely to have symptoms of depression.’’

But many teens said feeling popular and connected to friends is more important than a good night’s rest.

“When I’m texting someone I don’t feel alone,’’ said A.J. Shaughnessy, a ninth-grader at Boston College High School. “When you don’t have your phone, you feel incomplete.’’

Michael Joyce,16, a sophomore at the school, said the sound of his phone vibrating on his night table makes him happy. “Oh, good,’’ he thinks as he’s awakened, “someone’s texting me. Maybe someone needs me.’’

Sometimes teens answer late-night calls and messages less out of excitement than fear. In focus groups convened by the Pew Research Center, some teens related stories of friends or acquaintances who became angry or insulted when text messages or phone calls weren’t immediately returned. “As a result, many teens we heard from said they feel obligated to return texts and calls as quickly as possible, to avoid such tensions and misunderstandings,’’ the report said.

Indeed, Rich said he worked with one patient to come up with acceptable excuses for why she would not be available at midnight. “I suggested she discuss it with them in advance, and that an easy way to do it would be to tell them your parents take your phone away at night to charge it, or to put it on family rules, rather than to say, ‘I don’t do this anymore,’ which apparently has all kinds of implications.’’

Frank, of Case Western Reserve University, said parents should talk to their kids about unhealthy texting behavior, and, if necessary, consider restrictive actions such as confiscating phones overnight. But a 2010 Kaiser Family Foundation study found that “relatively few 7th-12th graders say their parents have established any rules about talking or texting on a cell phone.’’ Even parents who try to set limits find the teens determined not to unclench the phones.

“They say they need their phones as alarm clocks,’’ said Ashley Olaffson’s mother, Louise. “Or they tell me they need to charge their phones.’’

Shaughnessy’s mother, Leanne, has also talked to her child, with similar results.

“You can tell them all you want that there’s no reason be on the phone at 2 a.m.,’’ she said, “but after a certain point, unless you want to sit on top of them, you know it happens.’’

With thousands of texts to send and receive per month, who can afford to take the night off, even if it means dozing off in physics class? Nicole Giddings, 18, a senior at Norton High School, said she sometimes falls asleep during lectures.